Molecules and atoms are extremely small objects - both in
size and mass. Consequently, working with them in the laboratory
requires a large collection of them. How large does this collection
need to be? A standard needs to be introduced. This standard
is the "mole". The mole is based upon the carbon-12
isotope. We ask the following question: How many carbon-12 atoms
are needed to have a mass of exactly 12 g. That number is NA
- Avogadro's number. Thus, NA is defined by

NA x (mass of carbon-12 atom)
= 12 g

Careful measurements yield a value for NA = 6.0221367x10^+23.
This is an incredibly large number - almost a trillion trillion.
For example, if we stack NA pennies on top of one another how
tall would the stack be? The answer is it would be so tall that
the stack of pennies could reach the sun and back almost 500
million times!

A convenient name is given when there is an Avogadro's number
of objects - it is called a "mole". Thus in the above
example there was a mole of pennies.

1 mole = NA objects

The mole concept is no more complicated than the more familiar
concept of a dozen : 1 dozen = 12 objects. From the penny example
above one might suspect that the mass of a mole of objects is
huge. Well, that is true if we're considering a mole of pennies,
however a mole of atoms or molecules is a different story. Recall
that the atomic mass unit (amu) is defined
as 1/12 the mass of a carbon-12 atom. Consequently we have the
relation

NA x 12 amu = 12 g

Thus, a mole of carbon-12 atoms has a mass of just 12 g. What
about other atoms? In the periodic table the atomic mass of the
elements is given. For example the atomic mass of magnesium is
24.305 amu. This is the average isotopic mass of naturally occurring
magnesium. What is the molar mass of magnesium in grams? From
the equation above we get 1 amu = 1g/NA or 1 amu = 1.66054x10^-24
g. Thus, a mole of magnesium atoms has a mass of NA x 24.305
amu x (1.66054x10^-24 g/amu) = 24.305 g. A mole of magnesium
atoms has a mass of 24.305 g. This example demonstrates that
the atomic mass of magnesium can be interpreted in one of two
ways: (1) the average mass of a single magnesium atom is 24.305
amu or (2) the average mass of a mole of magnesium atoms is 24.305
g;